Yes, for all caudates.
Mind you, the sentence is not exact. The red coloration in caudates is entirely introduced by diet and then accumulated in xantophores. If they don´t get the pigments (carotenes) with the diet, the colour simply never develops. The thing is, that not all red foods are actually rich in carotenes. An excellent example of this are bloodworms. By looking at them one thinks "these couldn´t be redder, they must be chock-a-block with carotenes"...except that isn´t true. The bright red color of bloodworms comes from haemoglobin, which has absolutely nothing to do with the red color in caudates. They do have carotenes, but in a small proportion.
So the redder the food, the redder the belly, is not exactly true. It´s the richer in carotenes the food is, the redder the belly. The most natural and abundant source of carotenes for caudates are crustaceans in a variety of forms. They are not particularly red (some are more than others) and yet they are very rich in carotenes.